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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Honours Differential Equations (MATH10066)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 3 Undergraduate) AvailabilityAvailable to all students
SCQF Credits20 ECTS Credits10
SummaryCore course for Honours Degrees involving Mathematics.

This is a second course on differential equations discussing higher order linear equations, Laplace transforms, systems of First Order Linear ODEs, non-linear systems of ODEs, Fourier Series, use of separation of variables in standard PDEs and Sturm-Liouville Theory.

In the skills section of the course, we will work on symbolic manipulation, computer algebra, graphics and a final project. Platform: Python in computer labs.
Course description Syllabus : Systems of First Order Linear ODEs with constant coefficients using linear andmatrix algebra methods.
Numerical methods: Euler, Heun, RK
Nonlinear systems of ODEs: critical points, linear approximation around a critical point; introduction to nonlinear methods: Lyapunov functions.
Fourier series
PDEs by separation of variables
Sturm-Liouville theory
Laplace transform

Skills : Python brush up: functions, plotting.
Systems of 1st order ODEs: plotting phase portraits, using SciPy ODE solvers.
Nonlinear systems: exploring dynamical systems (limit cycles, chaos in the Lorenz model, in the periodically perturbed pendulum...) using SciPy ODEsolvers.
Numerical methods for ODEs: implementing Euler, Heun, etc.
Fourier: comparison function/truncated series, perhaps computation of Fourier coefficients.
PDEs: plots of 2D functions, animations.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Several Variable Calculus and Differential Equations (MATH08063) OR Introductory Fields and Waves (PHYS08053)
Prohibited Combinations Other requirements None
Information for Visiting Students
Pre-requisitesVisiting students are advised to check that they have studied the material covered in the syllabus of each pre-requisite course before enrolling.
High Demand Course? Yes
Course Delivery Information
Academic year 2023/24, Available to all students (SV1) Quota:  None
Course Start Semester 1
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 200 ( Lecture Hours 35, Seminar/Tutorial Hours 10, Supervised Practical/Workshop/Studio Hours 10, Summative Assessment Hours 3, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 138 )
Assessment (Further Info) Written Exam 70 %, Coursework 30 %, Practical Exam 0 %
Additional Information (Assessment) Coursework 30%, Examination 70%

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Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S1 (December)3:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Solve systems of linear ordinary differential equations, selecting the most appropriate method, including Laplace transform.
  2. Describe the behaviour of solutions of systems of nonlinear ordinary differential equations, locally by identifying critical points and determining their nature, and globally by identifying periodic orbits.
  3. Apply the method of separation of variables to solve simple linear PDEs (heat, wave and Laplace equations and similar), and demonstrate understanding of the Sturm-Liouville theory underpinning the method.
  4. Use appropriate symbolic and numerical methods in Python to solve and analyse differential equations.
  5. Carry out a small individual investigation, making use of Python, and produce a written report on the outcomes.
Reading List
Elementary Differential Equations and Boundary Value Problems, Boyce
and DiPrima, Wiley (continuing students should already have a copy from year 2).
Additional Information
Graduate Attributes and Skills Not entered
Course organiserDr Tom MacKay
Tel: (0131 6)50 5058
Course secretaryMiss Greta Mazelyte
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